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Our contribution sets out to investigate the phenomenology of a gauge modelbased on an $SU_{L}(2) \times U_{R}(1)_{Q} \times U(1)_{Q'}$-symmetry group.The model can accommodate, through its symmetry-breaking pattern, a candidateto a heavy $Z'$-boson at the TeV-scale. The extended Higgs sector introduces aheavy scalar whose mass lies in the region $1.2-3.7 \, \mbox{TeV}$. The fermionsector includes an exotic candidate to Dark Matter that mixes with theright-handed neutrino component in the Higgs sector, so that the whole fieldcontent ensures the cancellation of the $U(1)$-quiral anomaly. The masses arefixed according to the particular way the symmetry breaking takes place. Inview of the possible symmetry breakdown pattern, we study the phenomenologicalimplications in a high-energy scenario. We worek out the magnetic dipolemomentum (MDM) of the exotic fermion and the transition MDM due to its mixingwith the right-neutrino.

A $Z'$-model and the magnetism of a dark fermion candidate